The proleptic Gregorian calendar is produced by extending the Gregorian calendar backward to dates preceding its official introduction in 1582.
The proleptic Gregorian calendar is explicitly required for all dates before 1582 by ISO 8601:2004 (clause 3.2.1) if the partners to information exchange agree. It is also used by most Maya scholars, especially when converting Long Count dates (1st century BC – 10th century). However, neither astronomers nor non-Maya historians generally use it.
For these calendars we can distinguish two systems of numbering years BC. Bede and later historians did not use the Latin zero, nulla, as a year (see Year zero), so the year preceding AD 1 is 1 BC. In this system the year 1 BC is a leap year (likewise in the proleptic Julian calendar). Mathematically, it is more convenient to include a year zero and represent earlier years as negative, for the specific purpose of facilitating the calculation of the number of years between a negative (BC) year and a positive (AD) year. This is the convention used in astronomical year numbering and in the international standard date system, ISO 8601. In these systems, the year 0 is a leap year.
Although the nominal Julian calendar began in 45 BC, leap years between 45 BC and 1 BC were irregular (see Leap year error). Thus the Julian calendar with quadrennial leap years was only used from AD 1 until 1582 or later, so historians and astronomers prefer to use the actual Julian calendar during that period (see From Julian to Gregorian). But when seasonal dates are important, the proleptic Gregorian calendar is sometimes used, especially when discussing cultures that did not use the Julian calendar.
The proleptic Gregorian calendar is sometimes used in computer software to simplify the handling of older dates. For example, it is the calendar used by MySQL, SQLite, PHP, CIM, Delphi, and COBOL.
Difference between Julian and proleptic Gregorian calendar dates
Before the introduction of the Gregorian calendar, the difference between Julian and proleptic Gregorian calendar dates were as follows. Whenever the calendars do not have corresponding days, such as the Julian leap day missing from the proleptic Gregorian calendar or the ten days dropped when the Julian became the Gregorian calendar, the number of days that the calendars differ is undefined for few days. This table assumes a Julian leap day of 29 February, but the Julian leap day (the bissextile day) was ante diem bis sextum Kalendas Martias in Latin or 24 February (see Julian reform), so dates between 24 and 29 February in all leap years were irregular.
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